Mike and Ike are twins. Mike’s age is one more than twice a certain number. Ike’s age is 10 less than triple that same number. Find their ages.

Mike age is 3 less then twice the age of his brother nuke.
M = Mike's age now
N = Nuke's age now
M = 2N - 3

Ten years ago, four times nuke's age was one more mike's age.
M-10 = Mike's age 10 years ago
N-10 = Muke's age 10 years ago
4(N - 10) = 1 + M -10

what are their present ages

find M and N

substitute M = 2N - 3 into 4(N - 10) = 1 + M -10:

4(N - 10) = 1 + [2N - 3] - 10
4N - 40 = 2N - 12
2N = 28
N = 14

M = 2(14) - 3 = 28 - 3 = 25

Mike is 25 and Nuke is 14.

check:
4(14 - 10) = 4(4) = 16 = 26 -10 = 1 + 25 - 10